Of all the slaves of the Dark Lord, only the Nazgûl could have warned him of the peril that crept, small but indomitable, into the very heart of his guarded realm. But the Nazgûl and their black wings were abroad on another errand: they were... shadowing the march of the Captains of the West, and thither the thought of the Dark Tower was turned.

'I will take the Ring,' [Frodo] said, 'though I do not know the way.'....

[Elrond] said, 'I think that this task is appointed for you, Frodo; and that if you do not find a way, no one will. This is the hour of the Shire-folk, when they arise from their quiet fields to shake the towers and counsels of the Great.'

The Fellowship of the Ring, LoTR Book 2, Ch 2, The Council of Elrond

'If [the Ring] is destroyed, then [Sauron] will fall; and his fall will be so low that none can foresee his arising ever again. For he will lose the best part of the strength that was native to him in his beginning, and all that was made or begun with that power will crumble, and he will be maimed for ever, becoming a mere spirit of malice that gnaws itself in the shadows, but cannot again grow or take shape. And so a great evil of this world will be removed.'

Yet in that hour was put to the proof that which Mithrandir had spoken, and help came from the hands of the weak when the Wise faltered. For, as many songs have since sung, it was the Periannath, the Little People, dwellers in hillsides and meadows, that brought them deliverance.

For Frodo the Halfling, it is said, at the bidding of Mithrandir took on himself the burden, and alone with his servant he passed through peril and darkness and came at last in Sauron's despite even to Mount Doom....

The Silmarillion, Of the Rings of Power and the Third Age

At that moment Gollum... comes up and treacherously tries to take Ring. They wrestle and Gollum takes Ring and falls into the Crack.

Sauron Defeated — The End of the Third Age, HoME Vol 9, Ch 1, The Story of Frodo and Sam in Mordor

... there into the Fire where it was wrought [was] cast the Great Ring of Power, and so at last it was unmade and its evil consumed.

Then Sauron failed, and he was utterly vanquished and passed away like a shadow of malice; and the towers of Barad-dûr crumbled in ruin, and at the rumour of their fall many lands trembled.